I have a drawer with 4 shirts, 5 pairs of shorts, and 6 pairs of socks in it. If I reach in and randomly remove three articles of clothing, what is the probability that I get one shirt, one pair of shorts, and one pair of socks? (Treat pairs of socks as one article of clothing.)
Explanation: First, we can find the denominator of our fraction.  There are a total of $\dbinom{15}{3}=455$ ways to choose 3 articles of clothing out of 15. To find the numerator, we need to count the number of ways to choose one piece of each type of clothing.  There are 4 ways we can choose a shirt, 5 ways we can choose a pair of shorts, and 6 ways we can choose a pair of socks, making a total of $4\cdot 5 \cdot 6=120$ ways to choose a shirt, pants, and socks so our final probability is $\frac{120}{455}=\boxed{\frac{24}{91}}$.